- #1

pollytree

- 14

- 0

## Homework Statement

There are two log properties that I have to prove:

1) Explain why ln(b

^{1/n})=(1/n)ln(b) for b>0, set b=a

^{n}

2) Explain why ln(a

^{r})=rln(a) for any r in Q and a>0, ie r is rational.

## Homework Equations

ln(a

^{n})=nln(a)

## The Attempt at a Solution

In a previous question I have already proved that ln(a

^{n})=nln(a), where n is a natural number. What I'm unsure about, is how is this any different? For 1), I'm not sure why you set b=a

^{n}? Wouldn't you get ln((a

^{n})

^{1/n}) = ln(a)? I'm not sure how this helps me find the solution.

Similarly for 2), I'm unsure how it is any different to proving that ln(a

^{n})=nln(a).

Any help would be great!